Asymptotic Analysis and Summability of Formal Power Series
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Publication:4644994
DOI10.1007/978-3-319-52842-7_4zbMath1406.30002OpenAlexW2639440630MaRDI QIDQ4644994
Publication date: 9 January 2019
Published in: Trends in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-52842-7_4
integral transformsasymptotic expansionsCarleman ultraholomorphic classessummability of formal power series
Asymptotic theory of functional-differential equations (34K25) Power series (including lacunary series) in one complex variable (30B10) Series solutions to PDEs (35C10) Asymptotic expansions of solutions to PDEs (35C20) General theorems on summability (40D05) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)
Related Items
Summability of formal solutions for a family of linear moment integro-differential equations, Some notes on moment partial differential equations. Application to fractional functional equations, Estimates of formal solutions for some generalized moment partial differential equations, Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders, Solutions of linear systems of moment differential equations via generalized matrix exponentials, Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations, Differentially large fields, On sequences preserving \(q\)-Gevrey asymptotic expansions, Summability of formal solutions for some generalized moment partial differential equations, Summability of formal solutions for a family of generalized moment integro-differential equations
Cites Work
- Strongly regular sequences and proximate orders
- Strongly regular multi-level solutions of singularly perturbed linear partial differential equations
- Accelero-summation of the formal solutions of nonlinear difference equations
- Quasi-analyticity in Carleman ultraholomorphic classes
- On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities
- Summability and fractional linear partial differential equations
- Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform
- Log-convex sequences and nonzero proximate orders
- Problèmes de modules pour des équations différentielles non linéaires du premier ordre
- On the summability of formal solutions of linear partial differential equations
- Monomial summability and doubly singular differential equations
- On the summability of formal solutions of nonlinear partial differential equations with shrinkings
- On the multisummability of divergent solutions of linear partial differential equations with constant coefficients
- Smooth solutions of quasianalytic or ultraholomorphic equations
- Exact asymptotics of nonlinear difference equations with levels 1 and \(1^{ + }\)
- On E. Borel's theorem
- Multisummability of formal power series solutions of nonlinear meromorphic differential equations
- Surjectivity of the restriction map to a compact in classes of ultradifferentiable functions
- From divergent power series to analytic functions. Theory and application of multisummable power series
- A new proof of summability of formal solutions of nonlinear meromorphic differential equations
- Division by flat ultradifferentiable functions and sectorial extensions
- Summation of formal solutions of a class of linear difference equations
- Multisummability of formal solutions of singular perturbation problems
- Multisummability of formal solutions of some linear partial differential equations
- Multisummability of formal power series solutions of partial differential equations with constant coefficients
- Formal power series and linear systems of meromorphic ordinary differential equations
- Summability of formal solutions of linear partial differential equations with divergent initial data
- Flat functions in Carleman ultraholomorphic classes via proximate orders
- On Gevrey solutions of threefold singular nonlinear partial differential equations
- Summability in general Carleman ultraholomorphic classes
- Extension operators in Carleman ultraholomorphic classes
- Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients
- Stieltjes moment problem in general Gelfand–Shilov spaces
- An Extension Theorem of Whitney Type for Non Quasi-Analytic Classes of Functions
- Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
- LINEAR CONTINUOUS EXTENSION OPERATORS FOR GEVREY CLASSES ON POLYSECTORS
- Extension maps in ultradifferentiable and ultraholomorphic function spaces
- Extension Gevrey et rigidité dans un secteur
- Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients
- On singularly perturbed small step size difference-differential nonlinear PDEs
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